I have seen 11,000 written as １万１０００, but not as １.１万 (the way one may write '3.5 millions'). Is this possible?
Yes, we do sometimes utilize a large number as a unit for brevity, and of course it is customary to use powers of 104 (万, 億, 兆...) in Japanese, instead of those of 103 (thousand, million, billion...).
The decimal representation could be seen everywhere I think the English counterpart would be used except when the discrepancy of order matters; for example, beneath a viral tweet usually shown:
which is in the Japanese UI:
where you can see a decimal is followed by 万 (ten thousand).
As an aside, in some fiscal or statistical documents they use 103 scale (such as 123.4千円 or 56.7百万人), in order to align the order with the international convention. But this is quite unusual practice outside the field.
I think you can but it's somewhat uncommon in general usage. However, it can be used often in some scenarios such as when one is renting a property. Here are some examples I found:
人口1.1万（2010）(From the デジタル大辞泉 entry for the city of 夕張)
仕事後の寄り道 月1.1万円 (From a Nikkei article)
家賃5.5万円以下物件特集ページ (From a rental page)
If you put 1.1万 into google you will see how it can be used. It is possible to use it but from all of the examples I saw on the first 5 pages of google it seems to mostly be used in a statistic rather than normal messages or replies. So if you are putting it in a statistic I would say it is ok, other wise 1万1千 seems to be the go to or just 11,000.
Hope it helps.